Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session H12: Non-Linear Dynamics: Coherent Structures II |
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Chair: Jeff Tithof, University of Rochester/University of Minnesota Room: 303 |
Monday, November 25, 2019 8:00AM - 8:13AM |
H12.00001: Energy cascades and the asymmetric motion of coherent structures Douglas Kelley, Jeffrey Tithof, Gerrit Horstmann, Balachandra Suri, Hussein Aluie, Michael Schatz, Roman Grigoriev We present evidence for a connection between energy cascades, which transfer energy among length scales in turbulent flows, and the Lagrangian coherent structures (LCS), which describe passive scalar transport in flows. LCS come in two types, which mark regions of strongest nonlinearity in forward- and backward-time flow, respectively. But prior observations have shown a time asymmetry: in two-dimensional (2D) weakly turbulent flow, backward-time LCS move around more than forward-time LCS. We link that asymmetry to energy cascades. We show that a prescribed toy-model flow with the same asymmetry transfers energy to larger length scales, as in real 2D flow, but a prescribed flow with the opposite asymmetry transfers energy to smaller scales, which is non-physical. We also show that in three-dimensional (3D) simulations and in a 3D prescribed flow, the asymmetry of LCS motion is reversed along with the cascade direction, such that forward-time LCS move around more if and only if energy cascades to smaller length scales, as in real 3D flow. Our results suggest a deep connection between the irreversibility of LCS motion and the energy cascade direction, and could contribute to forecasting LCS dynamics. [Preview Abstract] |
Monday, November 25, 2019 8:13AM - 8:26AM |
H12.00002: Relating 2D and 3D Lagrangian coherent structures in oceanic flows H M Aravind, G. Salvador-Vieira, Vicky Verma, Sutanu Sarkar, Michael Allshouse Lagrangian coherent structures (LCS) techniques reveal elliptic structures that partition the domain into minimally- and well-mixed regions (Jupiter's Great Red Spot, Polar Vortex), and hyperbolic structures that are highly attracting/repelling material surfaces (long filaments of the Deepwater Horizon oil spill). These techniques can be applied to 3D ocean flows; however, the high computational cost of calculating 3D LCS or the lack of an accurate vertical velocity model often prove to be prohibitive. Hence, identifying when a 2D calculation captures the 3D LCS is beneficial. Sulman et al. (2013) introduced two diagnostic metrics -- the maximum vertical shear magnitude in horizontal velocities and the vertical velocity gradient -- to identify when 2D calculations of the finite-time Lyapunov exponent (FTLE) field are insufficient to capture the 3D hyperbolic LCS in steady, analytic flows. In our study, we investigate how well Lagrangian extensions of these metrics identify regions where 2D approximations for hyperbolic and elliptic LCS sufficiently represent the full structure. For this, we compare 2D FTLE and trajectory-clustering structures with 3D results for a high-fidelity, submesoscale simulation of an oceanic density front. [Preview Abstract] |
Monday, November 25, 2019 8:26AM - 8:39AM |
H12.00003: Vortex boundaries as barriers to vorticity transport in two-dimensional flows Stergios Katsanoulis, Mohammad Farazmand, Mattia Serra, George Haller Recent advances have revealed barriers to diffusive transport as material curves that inhibit the transport of diffusive scalars more than neighboring curves do. Extending these results, we discuss a new, fully frame-independent (objective) vortex identification method for two-dimensional flows. Our method locates vortex-core boundaries as closed material curves that inhibit the diffusion of vorticity more than other nearby material curves do. The exact solution to this calculus of variations problem provides a criterion that unites common features of empirical observations: the material and vorticity-transporting nature of observed vortex cores. We also discuss an algorithm, along with a publicly available numerical package, that enables the automatic extraction of maximally vorticity-preserving, material vortex cores from two-dimensional data sets. We conclude by demonstrating this algorithm on explicit Navier-Stokes solutions and two-dimensional turbulence simulations. [Preview Abstract] |
Monday, November 25, 2019 8:39AM - 8:52AM |
H12.00004: Material barriers to the transport of momentum and vorticity George Haller Recent work has identified objective (frame-indifferent) material barriers that are the least impermeable to the diffusion of passive scalars in turbulent flows. Here we discuss the extension of these results to identify material barriers to the transport of active quantities, such as vorticity and momentum, in three-dimensional unsteady flows. Challenges in such an extension include the vectorial nature of these active quantities, as well as their dependence on the frame of reference. With these challenges addressed, we obtain a general algorithm for locating objective material barriers to active transport, which form a dynamical skeleton around possible pathways in the flow. We illustrate the results on closed-form solutions of the Navier-Stokes equations, and well as on three-dimensional numerical simulations. [Preview Abstract] |
Monday, November 25, 2019 8:52AM - 9:05AM |
H12.00005: Stochastic Lagrangian Dynamics of Vorticity in Wall-Bounded Flows: General Theory Gregory Eyink, Akshat Gupta, Tamer Zaki The Lagrangian properties of vorticity for a smooth Euler solution have been extended to Naver-Stokes solutions by Constantin-Iyer (2008,2011) using a stochastic Lagrangian approach. This is best understood within the Kuz'min-Oseledets formulation of Navier-Stokes, in terms of the ``vortex-momentum'' associated to a continuous distribution of infinitesimal vortex rings. This theory provides an infinite set of exact Lagrangian conservation laws for Navier-Stokes vorticity, the ``stochastic Cauchy invariants''. These are preserved only backward in time, due to the irreversibility of Navier-Stokes dynamics. For wall-bounded flows, these invariants allow a complete representation of interior vorticity in terms of vorticity generated at a solid wall, as it is advected, stretched and rotated by the flow. We present a Monte Carlo method to calculate the stochastic Cauchy invariants and their statistics by solving the SDE's for ensembles of stochastic Lagrangian particles. We test the method using a space-time database of turbulent channel-flow at $Re_\tau=1000,$ verifying the conservation of mean values of the stochastic Cauchy invariants. Their variances grow exponentially in time, reflecting Lagrangian chaos in the channel flow and implying large cancellations in the conserved means. [Preview Abstract] |
Monday, November 25, 2019 9:05AM - 9:18AM |
H12.00006: Stochastic Lagrangian Dynamics of Vorticity in Wall-Bounded Flows: Turbulent Channel-Flow Akshat Gupta, Gregory Eyink, Tamer Taki We exploit an exact stochastic Lagrangian formulation of Navier-Stokes to study vorticity dynamics in a turbulent channel-flow at $Re_\tau=1000.$ ``Stochastic Cauchy invariants'' are conserved on average backward in time along stochastic Lagrangian particle trajectories, even as individual vorticity vectors are advected, stretched and rotated. At close prior times, conservation requires delicate cancellations between vorticity contributions from particles in the interior of the flow and those which strike the wall and remain fixed there. Far back in time, interior vorticity is represented by an average over vorticity that originated entirely at the wall. As in superfluids, cross-stream transport of tangential vorticity generated at the wall is exactly related to drag. We show that the process of vortex-lifting in the buffer layer is not an abrupt lifting of discrete vortex lines but is instead distributed over 100's of viscous times and 1000's of wall units. Despite simple arrays of ``hairpin'' vortex-lines, the dynamics involves intense competition between nonlinear Lagrangian chaos that exponentially magnifies \& rotates vorticity and strong viscous destruction. We discuss the Lighthill-Morton theory of vorticity generation from this stochastic Lagrangian perspective. [Preview Abstract] |
Monday, November 25, 2019 9:18AM - 9:31AM |
H12.00007: True topology of 3D unsteady flows with spheroidal invariant surfaces Michel Speetjens, Sebastian Contreras, Herman Clercx Scope is the response of Lagrangian flow topologies of 3D time-periodic flows consisting of spheroidal invariant surfaces (ISs) to perturbation. Such ISs have intra-surface Hamiltonian topologies comprising of islands and chaotic seas. Computational studies predict a response to perturbation dramatically different from the classical case of toroidal ISs: said islands and chaotic seas evolve into `tube-and-shell' structures by `resonance--induced merger' (RIM). This study provides conclusive experimental proof of RIM and advances the corresponding structures as the true topology of realistic flows with spheroidal ISs; the latter are singular entities that exist only for ideal conditions. Theoretical analysis reveals that RIM ensues from perturbed periodic lines via two possible scenarios: truncation of tubes by (i) manifolds of isolated periodic points emerging near elliptic lines or by (ii) segmentation of lines into elliptic and hyperbolic parts. This furthermore demonstrates that RIM indeed accomplishes tube-shell merger by exposing the existence of ISs that smoothly extend from tubes into chaotic shells. These phenomena set the response to perturbation -- and true topology -- of flows with spheroidal ISs fundamentally apart from flows with toroidal ISs. [Preview Abstract] |
Monday, November 25, 2019 9:31AM - 9:44AM |
H12.00008: Critical point identification in 3D velocity fields. Mohammadreza Zharfa, Paul S. Krueger Classification of flow fields involving strong vortices such as those from bluff body wakes and animal locomotion can provide important insight to their hydrodynamic behavior. Previous work has successfully classified 2D flow fields based on critical points of the velocity field and the structure of an associated weighted graph using the critical points as vertices. The present work focuses on extension of this approach to 3D flows. To this end, we have used the Gauss-Bonnet theorem to find critical points and their indices in 3D vector field, which functions similarly to the Poincare-Bendixson theorem in 2D flow fields. The approach utilizes an initial search for critical points based on local flow field direction, and the Gauss-Bonnet theorem is used to refine the location of critical points by dividing the volume integral from of the Guass-Bonnet theorem into smaller regions. To verify this approach, we have applied this method on some flow fields generated from potential flow theory and numerical methods. [Preview Abstract] |
Monday, November 25, 2019 9:44AM - 9:57AM |
H12.00009: Spectral reconstruction of incompressible flows and application to incomplete flow measurements Siavash Ameli, Shawn Shadden A wide range of fluid flow applications are incompressible. Noise in flow measurements is the main source that violates the divergence-free condition for such flows. A variety of approaches have been proposed to filter noise and reconstruct data. Proper Orthogonal Decomposition, Dynamic Mode Decomposition, radial basis functions and smoothing kernels and spectral filtering by Fourier representation are a few examples. Yet, for many applications the necessity of an incompressible projection is important. Previously, we have presented the spectral representation of vector fields that addresses incompressibility by means of orthogonal family of solenoidal fields. The spectral representation of the fluid flow is obtained by the projection of the flow to the eigenmodes that are generated for a specific geometry and satisfy a flow boundary condition. In this talk, we discuss the optimality of the set of eigenfunctions in modal reduction and representation of incompressible flows. Also, we will present modal reconstruction of ill-defined problems and demonstrate results on incomplete measurements of noisy flows. [Preview Abstract] |
Monday, November 25, 2019 9:57AM - 10:10AM |
H12.00010: Learning the Tangent Space of Dynamical Instabilities from Data Antoine Blanchard, Themistoklis Sapsis The optimally time-dependent (OTD) modes are a set of deformable orthonormal tangent vectors that track directions of instabilities along any trajectory of a dynamical system. Traditionally, these modes are computed by a time-marching approach that involves solving multiple initial-boundary-value problems concurrently with the state equations. However, for a large class of dynamical systems, the OTD modes are known to depend ``pointwise'' on the state of the system on the attractor, and not on the history of the trajectory. We leverage the power of neural networks to learn this ``pointwise'' mapping from phase space to OTD space directly from data. The result of the learning process is a cartography of directions associated with strongest instabilities in phase space, as well as accurate estimates for the leading Lyapunov exponents. [Preview Abstract] |
Monday, November 25, 2019 10:10AM - 10:23AM |
H12.00011: Search and Rescue at Sea Aided by Hidden Flow Structures Mattia Serra, Pratik Sathe, Irina Rypina, Anthony Kirincich, Shane Ross, Pierre Lermusiaux, Thomas Peacock, Arthur Allen, George Haller Every year hundreds of people die at sea because of vessel and airplane accidents. Using recent mathematical results for assessing short-term material transport in unsteady flows, we uncover hidden TRansient Attracting Profiles (TRAPs) in ocean-surface velocity data. Computable from a single velocity-field snapshot, TRAPs act as short-term attractors for all floating objects. We emulate SAR scenarios in three different ocean field experiments, and show that TRAPs computed from measured as well as modelled velocities attract deployed drifters and manikins emulating people fallen in water. TRAPs, which remain hidden to prior Eulerian diagnostics, thus provide critical information for hazard responses, such as SAR and oil spills, and have the potential to save life and limit environmental disasters. [Preview Abstract] |
Monday, November 25, 2019 10:23AM - 10:36AM |
H12.00012: Turbulent Flow in the Vicinity of Retaining Walls: Conditions at the Early Stages of Local Scour Development Nasser Heydari, Panayiotis Diplas, J. Nathan Kutz Turbulent flow characteristics corresponding to the initial stages of local scour development are investigated in the vicinity of a retaining wall structure. Data collection is performed using a volumetric particle image velocimetry to measure the three-dimensional velocity fields. Time-averaged flow topology, turbulence statistics, and instantaneous fields are examined. Furthermore, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) tools are applied to further understand the underlying features of the large-scale coherent structures around the obstruction. The results indicate that a horseshoe vortex (HV) system develops over the channel bank at the upstream face of the obstruction. It follows the sloping junction line towards the toe of the channel bank and then bends in the direction of the flow. It was indicated that turbulent kinetic energy (TKE) inside the HV system and bed shear stress values in the mean flow are more pronounced near the leading edge of the protrusion where the flow acceleration is the strongest. Consistently, the leading POD and DMD modes indicate that the HV captures a significant portion of the TKE content. They also confirm the aperiodic behavior of the HV system. [Preview Abstract] |
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